Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure : influence of noise

Baptiste Bergeot 1, 2 André Almeida 1 Christophe Vergez 2 Bruno Gazengel 1
2 Sons
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille] : UPR7051
Abstract : This paper presents an analysis of the effects of noise and precision on a simplified model of the clarinet driven by a variable control parameter. When the control parameter is varied the clarinet model undergoes a dynamic bifurcation. A consequence of this is the phenomenon of bifurcation delay: the bifurcation point is shifted from the static oscillation threshold to an higher value called dynamic oscillation threshold. In a previous work [8], the dynamic oscillation threshold is obtained analytically. In the present article, the sensitivity of the dynamic threshold on precision is analyzed as a stochastic variable introduced in the model. A new theoretical expression is given for the dynamic thresholds in presence of the stochastic variable, providing a fair prediction of the thresholds found in finite-precision simulations. These dynamic thresholds are found to depend on the increase rate and are independent on the initial value of the parameter, both in simulations and in theory.
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Baptiste Bergeot, André Almeida, Christophe Vergez, Bruno Gazengel. Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure : influence of noise. Nonlinear Dynamics, Springer Verlag, 2013, 74 (3), pp.591-605. ⟨10.1007/s11071-013-0991-8⟩. ⟨hal-00809293v4⟩

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